How to get the Controllpoints of the *hull* of a Bezier Curve?
Oh I see the confusion now. The handles of Bezier curve are the "real" control points. These points form the 4 control points for the cubic segment:



And that's also how you convert Bezier to BSplines - per segment. You can make a BSpline segment in Blender with Path curve with 4 points.

You get the described points with text like this:

bpy.data.curves['BezierCurve'].splines[0].bezier_points[1].handle_left
bpy.data.curves['BezierCurve'].splines[0].bezier_points[1].co
bpy.data.curves['BezierCurve'].splines[0].bezier_points[1].handle_right


Like this you get all the blue points.